Question

Jess's age is six years less than three times Ethan's age. The product of their ages is 45. What are their ages? Hint: Write an equation to represent the product of their ages, using x to represent Ethan's age, then solve this quadratic equation. Connect each person to their correct age.

Answer 1

Jess's age is six years less than three times Ethan's age. The product of their ages is 45. What are their ages?

Hint: Write an equation to represent the product of their ages, using x to represent Ethan's age, then solve this quadratic equation. Connect each person to their correct age.​

Let

x ------> Ethan's age

y -----> Jess's age

we have that

y=3x-6 -------> equation A

xy=45 ------> equation B

substitute equation A in equation B

x(3x-6)=45

solve for x

3x^2-6x=45

3x^2-6x-45=0

Solve using the formula

so

a=3

b=-6

c=-45

substitute

`x=\frac{-(-6)\pm\sqrt[]{-6^2-4(3)(-45)}}{2(3)}`
`\begin{gathered} x=\frac{6\pm\sqrt[]{576}}{6} \\ \\ x=(6\pm24)/(6) \end{gathered}`

the solutions for x are

x=5 and x=-3 (is not a solution)

Find the value of y

y=3(5)-6

y=9

therefore

Ethan's age is 5 years

Jess's age is 9 years